How can I Bevel this sphere correctly?
Update to the answer below
I see actually that it has 12 sides, so create 36 segments not 24, and change your edge selections accordingly and the 'Auto Smooth' value

I'm pretty new to Blender and I had a quick go at this using a feature I learned about today &quot;Auto Smooth&quot;.
Looking at the lampshade, it looks like it has 6 sides, so I created the UV sphere and before doing anything else at all, set the number of segments to 24. Please ignore the origin point as it's not important.

Then, I chose every 4th vertical edge using Alt+Left-Click for the first and Shift+Alt+Left-Click for each subsequent one.

Then using S and then Shift+Z so that only the x and y axes are scaled, I scaled those edges inwards toward the centre of the sphere.

Then I deselected them and selected each edge that was next to the edges I had just scaled:

And scaled them again using S and Shift+Z

OK. Getting close now. Go back to Object Mode and it still doesn't look quite right.

If I Right-Click on the sphere, and choose 'Shade-Smooth', that's no good because it smooths ALL the edges and you want to keep 6 of them sharp still. Leave the sphere smoothed at this point even though it looks wrong
I found out about Auto-Smooth and this might be what you're looking for.
Click on the Object Data tab - I'm using 2.90a, but if you're using 2.83, I think its in the same place...

Then click on the 'Normals' section and check the box next to 'Auto-Smooth' and I found that setting the angle value to 15.3 seems to produce what I suspect you want.